Abstract

In astrophysical regimes where the collisional excitation of hydrogen atoms is relevant,
the cross sections for the interactions of hydrogen atoms with electrons and protons
are necessary for calculating line profiles and intensities. In particular, at relative
velocities exceeding ~1000 km s^(−1), collisional excitation by protons dominates over
that by electrons. Surprisingly, the H-H+ cross sections at these velocities do not exist
for atomic levels of n ≥ 4, forcing researchers to utilize extrapolation via inaccurate
scaling laws. In this study, we present a faster and improved algorithm for computing
cross sections for the H-H+ collisional system, including excitation and charge transfer
to the n ≥ 2 levels of the hydrogen atom. We develop a code named BDSCx which
directly solves the Schrödinger equation with variable (but non-adaptive) resolution
and utilizes a hybrid spatial-Fourier grid. Our novel hybrid grid reduces the number
of grid points needed from ~4000n^6 (for a “brute force”, Cartesian grid) to ~2000n^4
and speeds up the computation by a factor ~50 for calculations going up to n = 4.
We present (l,m)-resolved results for charge-transfer and excitation final states for
n = 2–4 and for projectile energies of 5–80 keV, as well as fitting functions for the
cross sections. The ability to accurately compute H-H+ cross sections to n = 4 allows
us to calculate the Balmer decrement, the ratio of Hα to Hβ
line intensities. We find
that the Balmer decrement starts to increase beyond its largely constant value of 2–3
below 10 keV, reaching values of 4–5 at 5 keV, thus complicating its use as a diagnostic
of dust extinction when fast (~1000 km s^(−1)) shocks are impinging upon the ambient
interstellar medium.

Excitation and charge transfer in hydrogen-proton collisions at 5--80 keV and application to astrophysical shocks

Additional Information:

We are grateful to Avi Loeb for his help with getting the time
on the Odyssey cluster supported by the FAS Science Division
Research Computing Group at Harvard University. We
are also grateful to Mark Scheel for helping to get the time
on the SHC cluster at Caltech. D.T. and C.H. are supported
by the U.S. Department of Energy (DE-FG03-92-ER40701)
and the National Science Foundation (AST-0807337). C.H.
is supported by the David and Lucile Packard Foundation.
K.H. is supported by the Zwicky Prize Fellowship of the
Institute for Astronomy of ETH Zürich.